A Semiparametric Bayesian Approach to Destructive Weighted Poisson Cure Rate Model

Nonparametric or semiparametric Bayesian models are becoming increasingly popular in the context of cure rate or long term survival models. These models are more robust than their parametric counterparts. Rodrigues et al. (2010) proposed a Bayesian hierarchical destructive Poisson cure rate model to analyze survival data with a surviving fraction. This model assumes that the original number of lesions caused by risk factors is not getting fully recovered by the treatment and thus, it undergoes a destructive process. Moreover, these unrepairable fractions of lesions are competing to give rise to a tumor. In this research we propose a semiparametric counterpart of such models by relaxing the distributional assumption on the unobserved lifetimes. We model the unknown survival distribution with a Weibull Dirichlet Process mixture model, mixing on both the shape and scale parameters of the Weibull kernel, which results in a flexible mixture that can model a wide range of distributional shapes. We finally discuss the application of such model to cutaneous melanoma data.